An RPC endpoint is an access point to the Solana blockchain. A bit like a wifi access point gives you access to the internet.
Is each and every validator required to act as an ROC endpoint in
itself?
A node operator can choose to run its node as vote-only, RPC-only, or both simultaneously. This can be configured in the Solana runtime.
If so, can I just pick a "favorite" validator and send all my RPC traffic there?
You not only "can", but "need" to select an RPC endpoint, or it would be akin to want to access a wifi network without providing its SSID.
What might have confused you is that most Dapps hide this choice away from you by setting a default RPC for their app to work. Some give you a set of RPCs you can use, some let you input an arbitrary one (generally developer-oriented, like Solana and SolanaFM explorers for instance).
As a side note, the https://api.mainnet-beta.solana.com/ endpoint is a default endpoint yes, and the distinction to make between these and a paid one comes to rate-limiting. The public, free ones (there are others, from GenesysGo or Serum for instance) will typically severely limit your requests/second, while paid ones will allow you higher or unbounded rates. Selecting a free endpoint or subscribing to a paid one ultimately depends on what you are doing, the expected usage, and robustness required.